Framework for the Verification of Geometric Digital Twins: Application in a University Environment

Abstract

Digital Twins rely on accurate geometric models to ensure reliable representation, yet maintaining and updating these models remains a persistent challenge. This paper addresses one aspect of this challenge by focusing on the verification of photogrammetry-based models. It introduces a verification framework that defines measurable data quality elements and establishes conditions to assess whether model quality is maintained, improved, or degraded. Validation through a university building case study demonstrates the framework’s ability to detect quality differences between visually similar models. Meeting only one of the three verification conditions, the new model shows quality degradation, primarily due to reduced positional accuracy and resolution, making it unsuitable to replace the previous version used in the Digital Twin. Additionally, the developed web tool prototype enables the automated calculation of the framework’s verification scores. This study contributes to the growing discussion on Digital Twin maintenance by providing practical insights for improving the reliability of geometric models.

1. Introduction

Digital Twin technology has gained substantial attention in recent years, finding applications across diverse domains. At its core, a Digital Twin consists of three elements: the physical object (Physical Twin), its virtual representation (Digital Twin), and the bidirectional flow of data (Digital Thread) enabled by IoT devices [1]. The concept was first introduced by Dr. Michael W. Grieves at a Society of Manufacturing Engineering conference in October 2002 [2]. At that time, he described it as the “Conceptual Ideal for Product Lifecycle Management,” as the term “Digital Twin” had not yet been coined. The naming evolved over the years—from the “Mirrored Spaces Model” in 2005 to the “Information Mirroring Model” in 2006—before the term “Digital Twin” was formally adopted in 2010 during collaboration with NASA.

Researchers and industry practitioners have since identified various requirements for Digital Twins, including maturity levels [3,4], automation and autonomy [5], data integration [6], and learning capabilities [7,8]. Although a Digital Twin can never fully replicate its real-world counterpart, particularly in complex settings, it is designed to capture the essential characteristics of the physical environment and leverage collected data for service delivery or task optimization.

In the built environment, a Digital Twin is often defined as a digital replica of a building or infrastructure that functions as a central information repository, supporting storage, analysis, sharing, and service provision [1,9]. Services are typically defined based on the specific aspects or processes that need optimization. While developing a complex information system for simple tasks is rarely justified, implementing a Digital Twin becomes practical for complex assets or repetitive processes where the cost of information is lower than the cost of physical testing or wasted resources. ISO/IEC 30173:2023 provides examples of such services, including state analysis, simulation, and performance optimization [10].

The term “Geometric Digital Twin” (GDT) refers specifically to a 3D representation of the Physical Twin without incorporating semantic or relational information [11]. Creating or updating a GDT relies on Spatial and Visual Data (SVD) [12,13,14]. SVD includes point clouds, classified as spatial data, and images or video sequences, classified as visual data, typically captured using terrestrial or mobile scanners and cameras.

In university settings, Digital Twin supports a wide range of users. A small group, such as developers and operators, engages with the system at a technical level, while the broader community of students, staff, and visitors interacts with its services. These services include environmental visualization for orientation and navigation, as well as predictive maintenance of campus buildings and infrastructure to reduce operational costs. Within this context, the geometry of the Digital Twin is particularly important since it provides the spatial foundation upon which these services are built.

Photogrammetric models offer significant potential for creating campus-scale Digital Twins. Advances in image-based 3D scene capture have made it possible to generate detailed and textured models using even low-cost sensors such as smartphone cameras and Unmanned Aerial Vehicles (UAVs) [15]. Despite these advancements, errors can still occur during data collection, preprocessing, and modeling. Inaccuracies in geometric models can lead to spatial misalignment of data and unreliable visualization and analysis, directly affecting daily operations and long-term facility management on campus. Consequently, verifying model quality remains a critical and ongoing challenge, serving as a necessary precondition for the maintenance and updating of Digital Twins.

This paper addresses a specific aspect of this challenge by focusing on the verification of photogrammetry-based models. The research question is as follows: “How can the quality of a geometric model (the candidate model replacing an earlier version in the Digital Twin) be verified, and what workflow and conditions are required to support the verification process for long-term use?”. Therefore, the contributions of this paper are as follows:

• It defines measurable data quality elements for geometric model verification.
• It formulates explicit conditions for determining whether a geometric model maintains, improves, or degrades in quality.
• It provides a verification tool to calculate the scores and streamline the process.

The paper is organized as follows. The Background section reviews Digital Twin applications in university environments, current evaluation approaches, and data acquisition and measurement errors, as well as the accuracy and Level of Detail (LoD) of photogrammetry-based models. The Research Methodology section outlines the approach used for developing the framework, followed by the Framework for Verification of Geometric Digital Twins section, which presents the framework itself. The Results section demonstrates the framework’s implementation in a case study. The Discussion section reflects on the framework results, assesses them via alternative approaches, and highlights limitations and directions for future research. Finally, Appendix A and Appendix B provide detailed case study descriptions and present the prototype web application used for calculations.

2. Background

2.1. Digital Twins in University Environments

With growing interest in Digital Twin and its broad range of applications, many universities are investing in exploring, testing, and implementing technology to improve their environments and processes. At the University of Galway (Ireland), a 3D campus model was developed using surveys, photogrammetry, and façade photography [16]. The model was further enhanced with gaming technology to simulate dynamic shadows and weather effects. The goal of this creation was to support master planning, provide visualizations, and assist in traffic and pedestrian flow management. Although the system does not integrate real-time data and only provides spatial information, it can be considered a GDT for the campus environment.

At Western Sydney University (Australia), a Digital Twin is used to maintain the library by optimizing indoor environmental conditions, such as temperature, humidity, lighting, CO₂ levels, and TVOC concentration [17]. The system integrates a BIM model with a sensor network and is structured around a four-layer architecture: (1) data acquisition, (2) data communication and storage, (3) data and BIM integration, and (4) data analysis and visualization using semiotic representation. Although there are limitations, such as limited sensor coverage and an absence of performance simulations over time, the study emphasizes the practical application of Digital Twin technology in a university setting.

A dynamic Digital Twin was developed to support facility management at the Institute for Manufacturing, University of Cambridge (United Kingdom) [18]. The system integrates a BIM model, the building management system, and real-time sensor data, including temperature, humidity, lighting, CO₂, vibration, and occupancy monitoring. Its architecture consists of five layers: (1) data acquisition, (2) transmission, (3) digital modeling and data enhancement, (4) data-model integration, and (5) application. The study shows that a medium level of model accuracy (CityGML LoD 2–3 for the building and LoD 4 for specific areas or systems) is sufficient for supporting building maintenance.

A Digital Twin-based smart campus system was developed at Hubei University of Technology (China) [19]. The architecture combines a static spatial model with a dynamic data model. The static model includes a 3D representation of the environment, a behavioral model, and a set of simulation rules. The spatial data is organized in typical GIS layers such as terrain, roads, buildings, vegetation, and water. The dynamic model focuses mainly on synthetic simulation data, incorporating virtual and augmented reality. However, at the stage described in the study, the Digital Twin served primarily as a visualization and had not yet incorporated real-time sensor data.

The University of Birmingham (United Kingdom) illustrates another approach to developing a smart campus [20]. The campus is presented through 360-degree views and photographs of key locations, including accommodation, academic buildings, and nearby urban facilities, with some buildings offering internal virtual tours. A similar visualization approach is used at Georgetown University (USA) [21], where 2D maps include a comprehensive set of points of interest such as campus entrances, academic and residential buildings, parking and transportation, ADA facilities, sustainability initiatives, and virtual tours.

Table 1. Overview of Digital Twin applications in universities.

University	Purpose of Digital Twin	Technologies Used	Real-Time Data Utilization	Real-Time Measured Parameters
University of Galway (Ireland) [16]	Visualization of master planning, traffic, and pedestrian flow	Geodetic surveys, photogrammetry, façade photography	no	n/a
Western Sydney University (Australia) [17]	Optimization of indoor environment, data analysis, and visualization	BIM model, IoT	yes	Temperature, humidity, lighting, CO2, TVOC
University of Cambridge (UK) [18]	Optimization of facility management	BIM model, building management system, IoT	yes	Temperature, humidity, lighting, CO2, vibration, occupancy
Hubei University of Technology (China) [19]	Visualization	3D models, photographs, simulation data, virtual and augmented reality	no	n/a
University of Birmingham (UK) [20]	Visualization	360-degree views, photographs	no	n/a
Georgetown University (USA) [21]	Visualization	2D maps, photographs	no	n/a

summarizes Digital Twin applications in universities and indicates that the technology is still in its early stages, with limited integration of real-time data and a primary focus on visualization. Although traditional maps and photographs are still widely used, the increasing volume of data and advancing technology will likely lead to the adoption of more sophisticated approaches.

2.2. Evaluation of Digital Twins

In the context of assessing the geometric models used in Digital Twins, there is currently no universally applicable evaluation framework. Since no single geometric representation can accommodate the diverse use cases of a Digital Twin, requirements for geometry representation and assessment are typically defined based on the specific needs of each application.

The geometric accuracy of Digital Twins for bridges generated from point clouds was analyzed in [22]. The study examines strategies to achieve the required Level of Geometric Accuracy (LOGA) and emphasizes the need for an evaluation framework to support twinning and model updates. The study highlights that elements of different scales may require distinct twinning techniques, and a single Digital Twin may, therefore, include multiple types of geometric representations. To address this, the authors propose a two-level approach: at the macro-level, deviations are assessed to identify broad areas with significant discrepancies, often caused by occlusion or noise during data acquisition; at the micro-level, deviations are analyzed at the component scale for detailed accuracy evaluation. The case study evaluates the accuracy of the model by summing errors from the laser scanner and the scanning and modeling processes. However, it does not analyze these errors separately or suggest ways to reduce them. Instead, it focuses on the aggregated value of the model’s represented accuracy. The study also reviews the models’ classification systems (Level of Development, Level of Detail, Level of Information, and Model Granularity), which are mostly design-focused and less adaptive for as-built models.

The concept of “Level of As-Is Detail” for Digital Twins of roads was introduced in [23], emphasizing the need for an evaluation framework for assets in the Use phase. The concept includes the Level of Geometric Representation (LoGR) and Level of Semantic Granularity (LoSG), as well as two sub-concepts: Level of Geometric Uncertainty (LoGU), reflecting the accuracy of geometric reconstruction, and Level of Semantic Uncertainty (LoSU), indicating the reliability of object classification. However, this concept is domain-specific and lacks quantitative assessment metrics. Similarly, a grading system for twinning heritage buildings from point clouds was proposed in [24], comprising the Grade of Generation (GoG) to capture model scale, the Grade of Information (GoI) for informational requirements, and the Grade of Accuracy (GoA) to classify deviations between the point cloud and BIM model. GoA is quantified using mean distance, median, and standard deviation. However, the study focuses primarily on the modeling process and relies on the BIM model as the reference baseline, which may not always be available for buildings in the Use stage.

Several studies highlight the importance of updating GDT [12,14,25]. The concept of Geometric Coherence, which measures the similarity between the geometries of Physical and Digital Twins, has also been introduced in [25]. Maintaining coherence requires detecting changes in the physical object before updating its digital counterpart. While the study emphasizes geometry updating, it provides no concrete guidelines, focusing instead on the types of geometric changes and technologies for capturing them. Current SVD-based approaches for updating GDT have been reviewed in [14], and a geometry-based object class hierarchy was proposed to support the updating process. In that study, geometry updating is considered part of the ongoing maintenance of Digital Twins throughout the building lifecycle, with a primary focus on the Construction and Use phases. Subsequent research provided a more detailed review of methods for constructing and maintaining the as-is geometry of building Digital Twins [12]. However, both studies primarily rely on point clouds and use the BIM model as a reference. Their review of image-based methods focused on CNN-based object detection, which enables the identification of frequently occurring objects and those requiring substantial digitization effort. While effective for models with object classification, the approach is less relevant when classification is absent or incomplete.

2.3. Data Acquisition and Measurement Errors

The construction of a GDT relies on data collected under a set of interrelated conditions (“complex of conditions”): the object (what is measured), the subject (who measures), equipment (measured by), method (how measured), and environment (where measured). Optimizing these conditions enhances data accuracy, while suboptimal conditions increase the likelihood of errors. During geometry updates, individual elements can be adjusted, but full consistency cannot be guaranteed. Figure 1 illustrates the main factors influencing data acquisition accuracy, including the complex of conditions, measurements, and error types.

According to the theory of measurement errors and uncertainties, measurements can be obtained either directly or indirectly (derived through calculations based on other measured values) [26]. In terms of precision, measurements can be of equal precision, conducted under nearly identical conditions (rare in practice), or of unequal precision, taken under varying conditions (more common). The numerical values of the errors of equal-precision measurements can be estimated based on the Arithmetic Mean, Mean Square Error, and the Mean Square Error of the Arithmetic Mean. Unequal-precision measurements are evaluated using Measurement Weights, the Weighted Arithmetic Mean, and the Mean Square Error of a Unit Weight.

Based on the source, the errors in measurements can be classified as follows:

• Instrument errors: Imperfect design of the equipment;
• Personal errors: Caused by the observer’s condition during work;
• External errors: Changes in the environment during the data collection;
• Methodological errors: Incomplete consideration of conditions or incorrect methodological approach.

In terms of quantity, the measurements can be necessary or redundant, where redundancy refers to additional measurements beyond the required minimum. Based on impact, the errors in measurements can be classified as follows:

• Gross errors: Large deviations exceeding permissible limits;
• Systematic errors: Appear in all measurements and follow a pattern, either constant or variable;
• Random errors: Caused by variations in conditions; they cannot be completely eliminated, but can be assessed through redundant measurements.

Systematic and random errors are both common and significant, capable of propagating from one error to another or cascading undetected.

To improve consistency in data acquisition and reduce errors during geometry updating,

Table 2. Classification of the data acquisition variables.

Controllable	Measurable
	Yes		No
	Yes	Object (what is being measured)	Equipment (measured by)
		Measurement type (precision, quantity)	Method (how measured)
		Measurement errors source	Subject (who is measuring)
	No	Measurement errors impact	Environment (where measured)
		Measurement errors behavior

organizes acquisition variables along two dimensions: measurability (whether a variable can be quantified) and controllability (whether it can be adjusted).

• Measurable and Controllable: Includes factors such as the measured object and measurement type (precision, quantity). These can be monitored and adjusted to ensure consistency across datasets (e.g., survey scope, coverage area, flight pattern, lighting).
• Measurable but Not Controllable: Refers to error sources, impacts, and behaviors that can be quantified and partly mitigated during data processing but not directly controlled during data acquisition.
• Controllable but Not Measurable: Refers to equipment calibration and consistent acquisition methods to reduce the occurrence of systematic errors.
• Not Measurable and Not Controllable: Includes the operator and environmental conditions, which cannot be quantified or controlled and may introduce gross or random errors.

2.4. Model Accuracy and Level of Detail

Accuracy refers to the extent to which the information in a model aligns with accepted or true values, making it a critical parameter for evaluating geometric models. Accuracy reflects overall data quality and the presence of errors, and it is typically assessed in terms of completeness, consistency, positional accuracy, and temporal quality [27]. Accuracy should not be confused with precision, which relates to the measurements taken during data acquisition [28]. High precision does not guarantee high accuracy, nor vice versa. Model accuracy is typically categorized into two types: measured accuracy, based on the standard deviation of raw measurements, and represented accuracy, based on the processed data.

Model accuracy is also independent of LoD; any LoD can be achieved at varying accuracy levels. If the model’s LoD is predefined, the required accuracy of measurements, equipment, and surveying methods can be determined retrospectively. Factors such as density of ground control data, surface reflectivity and occlusions, and flight height and pattern affect measured accuracy, while LoD depends on the resolution of the acquired data.

The concept of LoD originated in computer graphics, where complex geometries are simplified to enable real-time rendering, a process also known as geometric simplification, mesh reduction, or multi-resolution modeling. In the Digital Twin context, LoD serves not only to optimize visualization performance but also to ensure model usability and adherence to real-world features. Unlike graphics applications that switch between multiple LoDs, a Digital Twin usually operates with a single model defined at a specific LoD.

For photogrammetry-based models, LoD is driven by image quality and resolution, typically expressed as the Ground Sampling Distance (GSD)—the distance between two adjacent ground pixels. A smaller GSD indicates higher image resolution. After reconstruction, the Average Ground Resolution (AGR) reflects the effective 3D model resolution, which is usually coarser than GSD due to image overlap and processing algorithms. While GSD characterizes raw images, AGR better represents the final model and is, therefore, more relevant for evaluation. Some applications require high-resolution and high-quality imagery, but not a high level of accuracy. This is particularly true for updates, where the intent is to upgrade the image resolution but still use ground control data that may have been originally acquired with lower accuracy requirements.

The Open Geospatial Consortium’s CityGML standard defines a framework of five LoD (0–4) levels for 3D city models [29]. However, CityGML LoD definitions do not specify required features or their granularity. To address this gap, Biljecki et al. proposed six defining metrics for LoD: feature presence, feature complexity, spatio-semantic coherence, texture, dimensionality, and required attributes [30]. The concept was later refined for buildings with a 16-level classification, subdividing each of the original LoDs 0–3 into four levels [31].

Table 3. Summary of CityGML LoDs and Biljecki’s LoD classification [29,31].

CityGML LoD	Biljecki’s LoD Classification
LoD		Description	Minimal Feature Size
LoD 2 (detailed model with roof structures) Data source: UAV, airborne LiDAR, photogrammetry Scale: city, city district Positional accuracy: ~2 m	LoD 2.0	A coarse model with standard roof structures, large building parts	>4 m, 10 m2
	LoD 2.1		>2 m, 2 m2
	LoD 2.2	Requirements of LoD 2.0 and LoD 2.1, addition of roof superstructures
	LoD 2.3	The roof overhangs are longer than 0.2 m. The roof edge and footprints are in their actual locations	>2 m, 2 m2 and 0.2 m for roof overhangs
LoD 3 (model with architectural details) Data source: close-range photogrammetry, terrestrial LiDAR Scale: city district, architectural model (exterior) Positional accuracy: ~0.5 m	LoD 3.0	The roofs with the windows. Windows of dormers do not have to be acquired	>1 m, 1 m2
	LoD 3.1	All features below the roof are LoD 3.2, the roof is LoD 2.3	>1 m, 1 m2; 0.2 m for roof overhangs
	LoD 3.2	Architecturally detailed model with features larger than 1.0 m	>1 m, 1 m2; 0.2 m for roofs and walls; and >1 m, 1 m2 for openings
	LoD 3.3	The features of size larger than 0.2 m, including embrasures of windows	>1 m, 1 m2; 0.2 m for roofs and wall details

presents a summary of CityGML LoDs and Biljecki’s refined LoD classification, emphasizing the levels relevant for this study.

In summary, the use of Digital Twins in university environments largely focuses on visualization as an initial implementation step that serves a wide range of users. Simultaneously, image-based techniques have become the dominant method for creating models due to their cost-effectiveness and relative ease of use, particularly for buildings with long operational histories and no existing BIM models. However, updating spatial data in dynamic environments remains challenging due to the complexity of the process and the unavoidable errors that occur during data acquisition and model generation.

Despite these challenges, the need for model assessment and regular updating is increasingly emphasized by researchers across various domains, from large-scale infrastructure assets to detailed building components. For photogrammetry-based models, this task becomes even more complicated, not only because of issues of positional accuracy but also because of limitations in data resolution and the resulting achievable LoD. While photogrammetry-based models are widely adopted, their quality often varies due to camera specifications, acquisition methods and conditions, environmental obstacles, and computational constraints that may require geometry simplification to reduce model size.

Since geometric models form a critical part of the complex architecture of a Digital Twin by providing a spatial foundation for visualizing and aggregating data, it is essential to ensure that these models are reliable and accurately represent the physical environment. This necessity, in turn, leads to the need for regular or on-demand model updates and, consequently, a robust geometric model verification process. Such a process must ensure coherent versioning, confirming that the new model not only accurately represents the physical environment but also demonstrates sufficient quality to replace its predecessor.

3. Research Methodology

The framework for verification of GDTs has been developed and validated using the Design Science Research (DSR) methodology. DSR is a systematic approach for generating knowledge about specific problems and their potential solutions within a research context. The multi-step process for developing the framework is shown in Figure 2.

3.1. Problem Identification and Motivation

The research gap was identified through a systematic literature review, consultation with field experts, and case study analysis, and it is formalized as the lack of a structured, long-term usable approach for verifying the geometric component of Digital Twins, particularly those derived from photogrammetry. This need was also highlighted in a previous review focusing on updating geometric parameters for built assets [32]. Prior research consistently emphasizes the essential requirement for geometric models to accurately represent the state of their physical counterparts [11,12,14,22,25]. Therefore, the verification process must ensure that a newly created model maintains—or, ideally, improves—quality compared to the reference model, thereby making it suitable for subsequent updating. Consequently, a reliable geometric verification approach is critical for twinning and updating processes.

3.2. Research Objectives and Requirements

To develop a verification framework for GDTs, the following research objectives were established:

• RO1: Define the key data quality elements for GDT verification that are both measurable and adaptable to different geometric representations.
• RO2: Develop a verification pipeline, grounded in data quality elements, to produce results indicating either improvement or decline in model quality.
• RO3: Establish conditions to determine whether a model’s quality is maintained, improved, or degraded.

3.3. Design and Development of the Framework

The framework was developed through a multi-step theoretical process as follows:

• Sampling theory was applied to define the scope of data for assessment. The Digital Twins may contain various types of geometric representations, as well as both structured and unstructured data [22]. For unstructured data (e.g., 3D meshes, DSMs), the model scale was used to determine the sample. For structured data (e.g., classified point clouds, segmented models), feature-based sampling can be applied.
• ISO 19157-1:2023 was used as the basis for defining data quality elements, which were further refined to accommodate both structured and unstructured data types, as supported by [33,34,35]. To ensure case specificity, the elements were categorized as mandatory, conditional, or optional. Each data quality element was linked to measurable metrics and organized into three categories: error/correctness indicator, error/correctness rate, and error/correctness count.
• The relationship between model resolution and achievable LoD was formalized by drawing on the LoD definition from [31]. This formalization, coupled with model resolution verification based on GSD, provides a basis for assessing the degree of model simplification that occurs after data processing and model generation.
• Three verification conditions were established based on [15,35] to evaluate model accuracy, resolution, and LoD. These conditions function as decision rules for identifying whether a model’s quality is maintained, improved, or degraded.

3.4. Demonstration of the Framework

To demonstrate the framework’s usability, a prototype web-based tool was developed in Python 3.12.2 to automate calculations and generate a verification score [36]. The GDT Verification Tool compares two geometric models, G(0) (reference) and G(t) (new), applying the three verification conditions (accuracy, resolution, and LoD) to assess the new model’s suitability for replacing the previous version. The developed tool was then used to evaluate case study models and compare the quality of models from different epochs (2022 and 2024) (Supplementary Materials).

3.5. Evaluation of the Framework

The framework was evaluated through its application to a case study, confirming its feasibility in real-world scenarios and the sufficiency of the defined data quality elements. The obtained results were additionally verified using alternative approaches. For accuracy verification, the models were registered using the Iterative Closest Point algorithm, followed by RANSAC segmentation and calculation of cloud-to-cloud (C2C) distances for several planar walls. For LoD assessment, a sensitivity analysis was conducted across a range of pixel coverage factors. For resolution verification, 3D mesh parameters (the number of triangles, average triangle area, mesh surface area, and volume) were calculated to assess differences between models that may indicate simplification.

4. Framework for Verification Geometric Digital Twins

The initial step in verifying a GDT is the setup of the reference model, G(0), as shown in Figure 3. This process involves three mandatory steps: defining the verification sample, specifying data acquisition parameters, and selecting data quality elements. Each of these steps informs the model verification process and the final verification score.

The representative sample (“Sample Definition”) must be consistently determined for both the reference model, G(0), and the subsequent model, G(t), either based on scale or specific features. However, a feature-based approach is not feasible for geometric models lacking object segmentation and classification. In such cases, like the presented case study, a scale-based sampling method must be applied. To minimize noise and potential outliers caused by obstructions or temporary objects, the case study sample was scale-based and limited to a single building.

Since the models were created under a different complex of conditions that affects the measured accuracy, data acquisition parameters are considered separately for each model. These parameters include camera specifications (focal length, sensor width, and image width) and approximate flight height. This information is then used to calculate the theoretically achievable GSD and compare it with the model’s actual resolution.

The data quality elements, which serve as quantifiable verification metrics, depend on the sample type and must be consistently applied to both models. Accuracy is the only mandatory data quality element, enabling the initial assessment of overall model quality. Conditional elements, such as Commission, Omission, and Temporal Quality, primarily focus on structured models, allowing for the assessment of redundancy, missing data, or object misclassification. Optional data quality elements mainly address data schema compliance, particularly when specified in project requirements. The list of data quality elements for model verification is provided in

Table 4. Data quality elements for Geometric Digital Twin verification.

Type	Sub-Type	Data Quality Measure	Definition	Category	Applicable to the Sample
Mandatory data quality elements
Consistency	Accuracy	Positional absolute	Alignment of the model with real-world context	Correctness indicator	Feature-, scale-based
		Positional relative	Internal consistency of the model	Correctness indicator	Feature-, scale-based
Conditional data quality elements
Completeness	Commission	Excess feature	The feature is not correctly presented in the model	Error indicator	Feature-based
		Number of excess features	The number of features in the model that are incorrectly represented	Error count	Feature-based
		Rate of excess features	The number of incorrect features relative to the total number of features	Error rate	Feature-based
		Number of duplicate features	Total number of duplications within the model	Error count	Feature-based
	Omission	Missing features	The feature is missing in the model	Error indicator	Feature-based
		Number of missing features	Number of missing features that should have been presented in the model	Error count	Feature-based
		Rate of missing features	The number of missing features relative to the total number of features	Error rate	Feature-based
	Temporal Quality	Number of incorrectly classified features	The total number of incorrectly classified features	Error count	Feature-based
		Misclassification rate	The ratio of incorrectly classified features to the total number of features	Error rate	Feature-based
Interoperability	-	Interoperability compliance	Compliance with interoperability requirements	Correctness indicator	Feature-, scale-based
Generalization	-	LoD compliance	The degree to which the model meets the required LoD	Correctness indicator	Feature-, scale-based
Optional data quality elements
Consistency	-	Data schema compliance	The feature is compliant with the data schema	Correctness indicator	Feature-based
		Number of non-compliant features	Total number of features that are not compliant with the data schema	Error count	Feature-based
		Non-compliance rate	The number of features that are not compliant with the data schema relative to the total number of features	Error rate	Feature-based
	Temporal Quality	Temporal accuracy	Accuracy of the temporal attributes of the data	Correctness indicator	Feature-, scale-based

. For the case study presented in the paper, Accuracy and LoD compliance were selected as the main data quality measures for assessment.

The setup of both models, including the selection of data quality elements, their corresponding values, and the data acquisition parameters, informs the analysis of each model’s positional accuracy and resolution. This analysis is subsequently used to calculate the verification score. If all three verification conditions (model accuracy, model LoD, and model resolution) are met, it indicates that the new model, G(t), outperforms the reference model, G(0), and is suitable for model updating.

4.1. Model Accuracy Analysis

The model accuracy analysis is based on the positional absolute accuracy (A_abs) and positional relative accuracy (A_rel). To assess the consistency of model accuracy over time, the difference between these measures is evaluated as

$${\mathrm{D}}_{\mathrm{a}\mathrm{c}\mathrm{c}}=\left|{\mathrm{A}}_{\mathrm{r}\mathrm{e}\mathrm{l}}-{\mathrm{A}}_{\mathrm{a}\mathrm{b}\mathrm{s}}\right|,$$

(1)

$${\mathrm{A}}_{\mathrm{r}\mathrm{e}\mathrm{l}}=1-{\displaystyle \frac{{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{R}\mathrm{E}}_{\mathrm{G}\left(\mathrm{t}\right)}}{{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{R}\mathrm{E}}_{\mathrm{G}\left(0\right)}}},$$

(2)

$${\mathrm{A}}_{\mathrm{a}\mathrm{b}\mathrm{s}}=1-{\displaystyle \frac{{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\_\mathrm{G}\mathrm{C}\mathrm{P}}_{\mathrm{G}\left(\mathrm{t}\right)}}{{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\_\mathrm{G}\mathrm{C}\mathrm{P}}_{\mathrm{G}\left(0\right)}}},$$

(3)

where RMSRE_G(t) is Root Mean Square Reprojection Error for model G(t); RMSRE_G(0) is Root Mean Square Reprojection Error for model G(0); RMSE_GCP_G(t) is Root Mean Square Error of Ground Control Points in model G(t); and RMSE_GCP_G(0) is Root Mean Square Error of Ground Control Points in model G(0).

If two different GCP networks were used to georeference models G(0) and G(t), then RMSE_GCP_G(0) and RMSE_GCP_G(t) are calculated separately according to the equations in

Table 5. Calculation of positional accuracy of GCPs.

Mean Error	$\overline{\mathrm{x}}={\displaystyle \frac{\sum {\mathrm{X}}_{\mathrm{i}}}{\mathrm{n}}}$$; \overline{\mathrm{y}}={\displaystyle \frac{\sum {\mathrm{Y}}_{\mathrm{i}}}{\mathrm{n}}}$$; \overline{\mathrm{z}}={\displaystyle \frac{\sum {\mathrm{Z}}_{\mathrm{i}}}{\mathrm{n}}}$
Standard Deviation	${\mathsf{\sigma }}_{\mathrm{x}}=\sqrt{{\displaystyle \frac{\sum {({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{x}})}^2}{\mathrm{n}}}}$$; {\mathsf{\sigma }}_{\mathrm{y}}=\sqrt{{\displaystyle \frac{\sum {({\mathrm{Y}}_{\mathrm{i}}-\overline{\mathrm{y}})}^2}{\mathrm{n}}}}$$; {\mathsf{\sigma }}_{\mathrm{z}}=\sqrt{{\displaystyle \frac{\sum {({\mathrm{Z}}_{\mathrm{i}}-\overline{\mathrm{h}})}^2}{\mathrm{n}}}}$
RSME	${\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{X}}=\sqrt{{\displaystyle \frac{\sum {\left({\mathrm{X}}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}}$$; {\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{Y}}=\sqrt{{\displaystyle \frac{\sum {\left({\mathrm{Y}}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}}$$; {\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{Z}}=\sqrt{{\displaystyle \frac{\sum {\left({\mathrm{Z}}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}}$
RSME Horizontal	${\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{H}}_1}={\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{H}}_{\left(\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{d}\right)}}$ ${\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{H}}_2}=\sqrt{{{(\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{X}}}^2+{{\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{Y}}}^2)}$ ${\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{H}}=\sqrt{{{(\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{H}}_1}}^2+{{\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{H}}_2}}^2)}$
RMSE Vertical	${\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{V}}_1}={\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{V}}_{\left(\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{d}\right)}}$ ${\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{V}}_2}={\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{V}}_{\left(\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\right)}}$ ${\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{V}}=\sqrt{{{(\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{V}}_1}}^2+{{\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{{\mathrm{V}}_2}}^2)}$
RSME_GCPs	${\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{G}\mathrm{C}\mathrm{P}}=\sqrt{{{(\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{H}}}^2+{{\mathrm{R}\mathrm{S}\mathrm{M}\mathrm{E}}_{\mathrm{V}}}^2)}$

.

Condition 1 (Model Accuracy Verification) is met if

• D_acc < δ_D—the accuracy of model G(t) is consistent with reference model G(0),
• D_acc ≥ δ_D—the accuracy is inconsistent, indicating degradation in model G(t).

The threshold, δ_D, can be determined empirically, from the mean and standard deviation of D_acc across multiple geometry update cycles, or normatively, according to project-specific or regulatory requirements. In the case study presented in this paper, ASPRS Positional Accuracy Standards for Digital Geospatial Data, Annex B, was used to establish the threshold, δ_D [37].

Geometric Deviation Analysis

Geometric deviation analysis is performed based on model alignment. In the presented case study, CloudCompare was used to align the models and calculate deviations. This process helps distinguish true geometric changes from noise or processing artifacts and to identify any positional shift between the models. To identify significant deviations, a positional threshold, δ_pos, is applied:

$${\mathsf{\delta }}_{\mathrm{p}\mathrm{o}\mathrm{s}}=\mathsf{\mu }\pm 2\mathsf{\sigma },$$

(4)

where μ is the mean deviation, and σ is the standard deviation.

By the empirical rule (68–95–99.7), ~95% of deviations fall within $\mathsf{\mu }\pm 2\mathsf{\sigma }$. If deviations exceed δ_pos, this indicates misalignment or significant changes in geometry between models.

4.2. Model LoD Verification

Model LoD verification evaluates whether the resolution of model G(t) is sufficient to support the LoD required by the reference model, G(0). While the relationship between a model’s AGR and its LoD is not formally defined, a practical resolution threshold can be established to ensure that LoD-relevant features are reliably represented. To estimate the relationship between the model’s AGR and the minimal feature size required by the LoD, the following algorithm based on “pixel coverage” was used:

• The minimal feature size—representing the smallest features that must be presented in the model—was determined based on Biljecki’s LoD classification, specifically focusing on LoDs 2-3 for photogrammetry-based models.
• Minimal feature representation requirement—these features must be represented by more than 1–2 pixels in the source imagery. Features spanning only 1–2 pixels are considered unreliable due to image noise, blur, and reconstruction uncertainty.
• Pixel coverage for minimal features—the number of pixels required to reliably represent a feature of minimal size. A common practical approach is to ensure that a feature is covered by at least 3 to 5 pixels [38,39,40].
• For the purposes of these calculations, an assumption factor of 4 pixels is applied. This means the minimal feature size should span approximately 4 pixels in the imagery to ensure robust feature reconstruction.
• The LoD is then assigned based on the model’s AGR according to the following relation:

$$\mathrm{A}\mathrm{G}\mathrm{R}\left[\mathrm{m}\mathrm{m}/\mathrm{p}\mathrm{x}\right]={\displaystyle \frac{\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{l} \mathrm{f}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{z}\mathrm{e} \left[\mathrm{m}\mathrm{m}\right]}{\mathrm{P}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l} \mathrm{c}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r} \left[\mathrm{p}\mathrm{x}\right]}},$$

(5)

Thus, the model’s AGR indicates whether it can reliably represent LoD-relevant features. For example, a model achieving an AGR of 50 mm/px can capture features as small as 0.2 m (assuming a coverage factor of 4 pixels), making it sufficient for LoD 3.3 modeling.

Table 6. Model’s AGR values for LoDs 2.0–3.3 based on 4-pixel coverage factor.

LoD	Model’s AGR
LoD 2.0	1000 mm/px
LoD 2.1	500 mm/px
LoD 2.2
LoD 2.3	500 mm/px; 50 mm/px for roof overhangs
LoD 3.0	250 mm/px
LoD 3.1	250 mm/px; 50 mm/px for roof overhangs
LoD 3.2	250 mm/px; 250 mm/px for openings; 50 mm/px for roofs and walls
LoD 3.3	250 mm/px; 50 mm/px for roofs and walls details

provides the necessary model AGR values for LoDs 2.0–3.3, based on the defined minimal feature sizes and 4-pixel coverage factor.

Since AGR is an average approximation across the model, additional verification of LoD assignment includes comparing the actual dimensions of features within the model (e.g., roof edges, windows) against real-world measurements, which is expressed as RMSE.

Thereby, Condition 2 (Model LoD Verification) evaluates the assigned LoD based on the AGR value of the new model, G(t), against the reference model, G(0), and is satisfied when the LoD of G(t) is consistent with that of G(0).

4.3. Model Resolution Verification

Model resolution analysis compares the achieved resolution of models G(0) and G(t). The achieved resolution is calculated as the ratio of the theoretical GSD_calc (derived from flight and camera parameters) to the actual AGR obtained after model reconstruction. This ratio quantifies the degree to which the reconstructed model deviates from the theoretical resolution.

$${\mathrm{R}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_{\mathrm{a}\mathrm{c}\mathrm{h}\mathrm{i}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{d}}\left(\mathrm{\%}\right)={\displaystyle \frac{{\mathrm{G}\mathrm{S}\mathrm{D}}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}}{\mathrm{A}\mathrm{G}\mathrm{R}}}\times 100,$$

(6)

$${\mathrm{G}\mathrm{S}\mathrm{D}}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}\left[\mathrm{m}\mathrm{m}/\mathrm{p}\mathrm{x}\right]={\displaystyle \frac{\mathrm{H}\left[\mathrm{m}\right]\times {\mathrm{S}}_{\mathrm{w}}\left[\mathrm{m}\mathrm{m}\right]}{\mathrm{f}\left[\mathrm{m}\mathrm{m}\right]\times \mathrm{W}\left[\mathrm{p}\mathrm{x}\right]}}\times 1000,$$

(7)

where H is the flight height, S_w is the sensor width, f is the focal length, and W is the image width.

The achieved resolution ratio near 100% indicates that the model resolution closely matches the theoretical expectation; a ratio significantly below 100% signals a degraded resolution, meaning the reconstruction is coarser than expected. Condition 3 (Model Resolution Verification) is considered satisfied if model G(t) performs equal to or better than model G(0) regarding achieved resolution.

5. Results

5.1. Case Study Description

The Kaunas University of Technology (KTU) campus serves as the case study for validating the framework. As shown in Figure 4, the architecture of the KTU Digital Twin consists of IoT devices and APIs for real-time data collection, SVD for spatial context, and a deployment platform providing data aggregation and a user interface. The SVD includes panoramic photos, BIM models for individual buildings, CAD and GIS data for underground utilities, and a campus-scale photogrammetry model that acts as the main visualization environment. Since the 3D mesh serves as the primary spatial foundation for campus visualization, the need to maintain and regularly update this model to reflect changes in the physical environment is a practical challenge that must be addressed. A detailed description of the case study is provided in Appendix A and reference [41].

To validate the framework, two photogrammetry models of the same building from different years—model G(2022) and model G(2024)—were compared. Both data acquisition campaigns occurred while the building was in the Use phase, though part of it was undergoing refurbishment in 2022. Two types of quadcopters were used for image acquisition. In both campaigns, the flights were conducted at an average altitude of approximately 80 m, following an oblique grid pattern with 50% forward overlap and 60% side overlap. GCPs were used for georeferencing and measured with a GNSS RTK rover in the Lithuanian LKS-94 (EPSG:3346) coordinate system. Both datasets were processed using analytical aerotriangulation in Bentley’s iTwin Capture Modeler (formerly Context Capture). The computational setup included an Intel(R) Core(TM) i7-8700 CPU @ 3.20 GHz, 32 GB of RAM, and an NVIDIA Quadro P2000 GPU.

Table 7. Camera characteristics and aerotriangulation results for the G(2022) and G(2024) models.

Model Version	G(2022)	G(2024)
Camera	Hasselblad L1D-20c	DJI Mavic 2 Enterprise Advanced
Sensor size [mm]	13.2	6.4
Image dimensions [px]	5472 × 3648	8000 × 6000
Focal length (calibrated) [mm]	10.39	4.72
RSMRE [px]	0.67	1.49
AGR [mm/px]	20.764	23.242

presents the camera specifications and aerotriangulation results for the G(2022) and G(2024) models.

5.2. Model Accuracy Analysis

The model accuracy analysis was performed based on the RMSRE for tie points, which provides the relative positional accuracy, A_rel, by aligning the images and creating the 3D structure. The RMSE_GCP provides the absolute positional accuracy, A_abs, by anchoring the model to real-world coordinates. The GCPs ensure that the model is correctly positioned and scaled, correcting for any potential drift or misalignment that may occur when relying solely on tie points.

Two different networks of GCPs were used to georeference the models. The positional accuracy of the GCPs was calculated according to Table 5. The results of the calculations are presented in

Table 8. Positional accuracy of GCPs for model G(2022).

Number of GCPs = 7	Measured		Reprojected
	Horizontal Accuracy	Vertical Accuracy	Horizontal Accuracy, X	Horizontal Accuracy, Y	Vertical Accuracy, Z
Mean Error [m]	0.009	0.011	0.000	−0.001	0.002
Standard Deviation [m]	0.005	0.007	0.013	0.007	0.014
RSME [m]	0.011	0.013	0.013	0.007	0.014
RSMEH [m]	0.018
RSMEV [m]	0.019
RSME_GCP [m]	0.026

and

Table 9. Positional accuracy of GCPs for model G(2024).

Number of GCPs = 18	Measured		Reprojected
	Horizontal Accuracy	Vertical Accuracy	Horizontal Accuracy, X	Horizontal Accuracy, Y	Vertical Accuracy, Z
Mean Error [m]	0.016	0.023	−0.015	−0.004	0.000
Standard Deviation [m]	0.006	0.008	0.040	0.029	0.041
RSME [m]	0.018	0.025	0.043	0.029	0.041
RSMEH [m]	0.054
RSMEV [m]	0.048
RSME_GCP [m]	0.073

and are used to calculate the accuracy difference between the models (D_acc).

To assess the consistency of the models’ accuracy over time, the accuracy difference between models, D_acc, was calculated as 0.288. The corresponding threshold, δ_D, was set at 0.075, based on Table B.5 [32] and the model’s AGR. Since D_acc ≥ δ_D, this indicates inconsistent accuracy, with the new model, G(2024), demonstrating worse positional performance.

Geometric Deviation Analysis

Models G(2022) and G(2024) were aligned in the CloudCompare software to calculate the geometric deviations using the Cloud-to-Mesh (C2M) distance method, as illustrated in Figure 5. The resulting statistical analysis of the geometric deviation is presented in

Table 10. The statistical analysis of geometric deviation between G(2022) and G(2024).

Parameter	Mean [m]	Std Dev [m]	Variance [m]	Range [m]	Q1 [m]	Q3 [m]	IQR [m]
Value	0.039	0.145	0.021	1.500	0.025	0.774	0.750

.

The statistical analysis of the geometric deviations shows an average distance between G(2022) and G(2024) of approximately 0.039 m. Since the mean is positive, model G(2022) tends to lie slightly outside G(2024) on average. A standard deviation of 0.145 m indicates moderate variability in the distances, as shown in Figure 6. The total distance range is 1.500 m, spanning approximately −0.6 m to 0.9 m. This wide range suggests significant deviations at certain points. Visual analysis of the models confirmed that extreme deviations were caused by the vegetation and temporal objects near the building, creating obstructions that affected the model’s reconstruction. Further analysis shows that the majority of the values fall within the range of −0.100 m to 0.150 m. The first quartile (Q1) is 0.025 m, the third quartile (Q3) is 0.774 m, and the resulting interquartile range (IQR) is 0.750 m, representing the middle 50% of the data.

To filter out noise and identify significant deviations or misalignment, a threshold, δ_pos, was calculated as 0.331 m. For the geometric deviations, 96.40% of the values fall below δ_pos, indicating a high degree of alignment between Models G(2022) and G(2024).

5.3. Model LoD Verification

Condition 2 is validated using the actual AGR values obtained after model reconstruction and the assigned LoD, as defined in Table 6. The assigned LoD is further verified by calculating the RMSE of feature dimensions in the models compared to real-world measurements. Specifically, window dimensions were used as a reference to assess each model’s ability to preserve geometric details.

Based on their AGR values, 20.764 mm/px for G(2022) and 23.242 mm/px for G(2024), both models qualify for LoD 3.3. To confirm this assignment, the dimensions of 14 windows were measured on-site using a Leica Disto D2 laser distance meter, which has a measurement accuracy of ±1.5 mm/m. These measurements were then compared against the corresponding model values at each floor level.

As shown in

Table 11. RMSE of window dimension deviations per floor.

RSME [m]	G(2022)	G(2024)
4th floor	0.14	0.21
3rd floor	0.16	0.20
2nd floor	0.16	0.21
1st floor	0.18	0.20
Total	0.15	0.21

, the RMSE increases toward the lower floors, indicating reduced resolution at these levels. This effect is attributed to the flight pattern during data acquisition, which resulted in lower-quality imagery for the building’s lower sections. Furthermore, G(2022) demonstrates generally higher accuracy than G(2024), with an RMSE of 0.15 m compared to 0.21 m, suggesting that geometric features are captured in greater detail in the earlier model.

5.4. Model Resolution Verification

Condition 3 is validated by comparing the model’s AGR values with the theoretical GSD_calc, derived from flight and camera parameters. The ratio of AGR to GSD_calc expresses the extent to which the model resolution approaches the theoretical maximum. For model G(2022), the achieved resolution is 89.45%, indicating that the reconstructed model closely reflects the expected resolution. In contrast, model G(2024) achieves only 58.34%, demonstrating reduced performance and a higher degree of resolution loss.

Framework validation results for models G(2022) and G(2024) are presented in

Table 12. Framework validation results for models G(2022) and G(2024).

Condition	G(2022)	G(2024)	Interpretation
Condition 1: Model Accuracy Verification
Aabs [m]	0.026	0.073
Arel [px]	0.67	1.49
Dacc	0.288		Dacc ≥ δD—inconsistent accuracy, decline in G(2024)
δD	0.075
Geometric deviation analysis
δpos [m]	0.331		High alignment between models
% of deviations < δpos	96.40
Condition 2: Model LoD Verification
Assigned LoD	3.3	3.3	Consistent LoD for both models
Feature’s RSME [m]	0.15	0.21	Decline in G(2024) feature representation
Condition 3: Model Resolution Verification
Resolution achieved [%]	89.45	58.34	Resolution loss for G(2024)

. The comparison indicates that G(2022) outperforms G(2024) across all framework conditions except geometric alignment, where both models show a high degree of consistency. Specifically, model G(2024) demonstrates lower positional accuracy, higher feature RMSE, and a significant loss of resolution.

While visual inspection of models can provide an initial impression of quality and help identify major discrepancies, it does not capture subtle yet important differences. The quantitative metrics applied in the developed framework, therefore, allow for a more precise and objective assessment, particularly when evaluating visually similar models. The framework thus offers a structured approach for assessing the quality of photogrammetry-based models used in Digital Twins. To demonstrate its practical usability, the framework has been deployed as a prototype web application, accessible at [36]. A description of its application to the case study is provided in Appendix B.

6. Discussion

6.1. Assessment of the Framework’s Accuracy Analysis

To confirm the results of Condition 1, both models were first converted into point clouds and resampled to one million points each to ensure computational efficiency. The models were then registered using the Iterative Closest Point (ICP) algorithm, which aligns geometries by minimizing Euclidean point-to-point distances to achieve the best geometric fit between datasets, regardless of their reference systems. The resulting ICP RMSE of 0.398 m suggests a moderate level of initial agreement between G(2022) and G(2024). After registration, both point clouds were segmented using the Random Sample Consensus (RANSAC) algorithm, and four main wall planes were extracted from each model for Cloud-to-Cloud (C2C) distance analysis.

As shown in

Table 13. Calculation of the C2C distances for segmented walls.

Wall	Reference Model: G(2022)			Reference Model: G(2024)
	Mean [m]	Std Dev [m]	Max dist. [m]	Mean [m]	Std Dev [m]	Max dist. [m]
1	0.22	0.14	1.25	0.23	0.16	2.85
2	0.22	0.15	1.12	0.20	0.14	1.61
3	0.12	0.07	1.59	0.17	0.20	2.80
4	0.14	0.09	1.49	0.22	0.26	2.86

, the corresponding wall surfaces are nearly parallel in both models, with mean distances ranging from 0.12 to 0.23 m and relatively low variability (standard deviation 0.07–0.26 m). However, the reverse C2C analysis (using G(2024) as the reference) shows higher dispersion in maximum distances. This indicates that G(2024) aligns less precisely and has lower geometric accuracy. Because this analysis relies solely on local geometric correspondence and does not depend on external ground control data, it serves as an alternative validation approach, confirming the framework’s finding that G(2024) shows lower geometric accuracy compared to G(2022).

6.2. Assessment of the Framework’s LoD and Resolution Analysis

To assess the sensitivity of LoD assignment, the relationship between LoD and AGR was recalculated for pixel coverage factor values from 3 to 10. The results show that both datasets maintain sufficient AGR to support LoD 3.3 modeling for pixel coverage factors between 3 and 8. When the pixel coverage factor exceeds 9, the AGR of G(2024) drops below the LoD 3.3, remaining suitable only for LoD 3.0 representation.

For an alternative assessment of model resolution, several mesh-based metrics were calculated following the approach by Biljecki et al. [31]: total triangle count, average triangle area, surface area, and enclosed volume, as shown in

Table 14. Three-dimensional mesh metrics for models G(2022) and G(2024).

3D Mesh Metrics	G(2022)	G(2024)
Number of triangles	5,434,282	414,829
Avg. triangle surface [m2]	0.004	0.045
Total surface area [m2]	22,881.6	18,618.4
Volume [m3]	78,485.2	80,039.5

. Both models preserve a similar total volume (~80,000 m³), confirming that large-scale geometry remains consistent. However, G(2024) contains substantially fewer triangles (0.42 million vs. 5.43 million) and a significantly larger average triangle area (0.045 m² vs. 0.004 m²), resulting in a more generalized surface and reduced ability to represent fine architectural details.

6.3. Summary of Verification Results

Both the framework results and their verification through alternative approaches indicate a degradation in the quality of model G(2024). Although both models show a high degree of alignment (96.4% of geometric deviations between models are below the δ_pos threshold of 0.331 m), model G(2024) demonstrates lower positional accuracy based on ground control data (RMSE of 0.073 m vs. 0.026 m for model G(2022)) and a higher reprojection error for tie points (1.49 px vs. 0.67 px), indicating a less accurate reconstruction. These findings were further confirmed using alternative ICP registration and C2C distance calculations. Even without the influence of ground control data, G(2024) shows greater variability in distances and a wider maximum distance range, confirming its lower accuracy.

In terms of achievable LoD, the analysis showed that LoD compliance is the only condition where both models perform almost equally. While the AGR of both models is sufficient for LoD 3.3 modeling, the analysis of façade window dimensions compared with real-world measurements showed that features are slightly less preserved in model G(2024), with an RMSE of 0.21 m vs. 0.15 m for model G(2022). Since the AGR values are quite similar (23.242 mm/px for G(2024) and 20.764 mm/px for G(2022)), a sensitivity analysis of LoD assignment to different pixel coverage factors showed that the models perform similarly overall, diverging only when the pixel coverage factor exceeds 9 pixels.

Considering the model resolution, G(2024) again falls significantly behind G(2022), despite the use of a more advanced camera during data acquisition. Based on GSD calculations, G(2024) achieved only 58.34% of the theoretical resolution that the camera could provide, compared to 89.45% for model G(2022). Alternative mesh-based metrics of the reconstructed models further show a substantial difference in the number of triangles and their average size, while maintaining similar total volume and surface area. This significant difference in triangle count indicates a coarser reconstruction of G(2024), with greater geometric simplification and fewer preserved details.

In general, several factors explain the weaker performance of G(2024). Despite using more GCPs (18 vs. 7), G(2024) was produced as part of a large-scale campus survey (area = 3.59 km², 3856 images), whereas G(2022) was captured as a standalone model (area = 0.57 km², 1108 images). Large-area surveys typically require block adjustments during photogrammetric processing, which distribute residual errors across the entire model, consequently reducing local accuracy and resolution within sub-regions. In contrast, the higher image density, greater overlap, and denser GCP distribution relative to the survey size in G(2022) resulted in more precise georeferencing and higher spatial resolution.

6.4. Limitations and Future Work

The study acknowledges several limitations and outlines potential directions for future research. Regarding Condition 2, the established relationship between LoD and AGR should not be interpreted as definitive; rather, it provides a methodological pipeline to guide their alignment. Future research will focus on exploring the sensitivity of this alignment using data-driven approaches to determine optimal AGR thresholds for various LoDs.

The framework’s validation is also constrained by the characteristics of the case study, where both models were represented as unstructured 3D meshes and verification relied on scale-based sampling. Consequently, not all data quality elements—specifically those relevant for feature-based samples—were applicable. Nevertheless, the full list of data quality elements has been retained to support broader applicability in future projects involving different types of models.

To facilitate scalability from single-building analysis to multi-building assessments, future work will investigate the application of Dempster–Shafer theory (also known as the theory of belief functions or evidence theory). This approach can provide a formal mechanism for assigning belief to three states—perform, do not perform, and unknown—based on aggregated evidence from multiple conditions (accuracy, LoD, and resolution). Additionally, it enables dynamic calibration of deviation thresholds. For instance, the current empirical threshold of 95% may be overly strict when evaluating multiple geometric models of varying quality, and it can be refined through the evidence fusion process within Dempster–Shafer theory.

7. Conclusions

A Digital Twin integrates diverse and heterogeneous data sources, with geometric models playing a central role in providing contextual information. These models not only enable visualization but also support advanced applications such as monitoring, simulation, and prediction. However, maintaining and updating the geometric component of a Digital Twin is often neglected due to the high cost and effort associated with digitizing complex environments. Verifying the quality of geometric models is, therefore, a critical step before deciding whether updates are feasible and necessary.

This paper introduces a framework for the verification of GDT, validated using photogrammetry-based models of a university building. The framework specifies three conditions that must be met to verify a newly created model against a reference, enabling a clear determination of quality improvement or degradation. The validation results demonstrate that the proposed data quality elements and verification procedure are sufficient to detect and quantify differences in visually similar models. Based on the framework’s output, we conclusively showed that the new model, intended to replace the version currently used in the Digital Twin, was insufficient and of low quality compared with its predecessor. In addition, a calculation tool has been developed to support the long-term usability of the framework. Accordingly, in line with the research objectives, the developed framework demonstrates measurable data quality elements, proposes a verification workflow, and defines conditions to detect degradation or improvement in geometric model quality.

Although the proposed approach acknowledges certain limitations, including the lack of verification based on structured data, it nonetheless contributes to the broader discussion on the reliability of geometric models within Digital Twins. It provides practical guidance for both researchers and industry practitioners working with image-based methods to develop and deploy Digital Twins.